How To: 1 Bone Moves Entire Arm, While IK Bones Can Bend Arm
I think I found my own answer.
If I keep my target far enough away from the arm bones, the arm will stay stiff.  I could animate it that way, by moving it, say, 1.5 m away from the arm on its local Z axis.  When I want to bend it, I can move it in closer on the local Z axis.
Whether this is an efficient method, I don't know, but I think it will work for me.
I am going to leave this question open for other suggestions at this time.